Question

WILL RATE IMMEDIATELY!

PLEASE EXAMINE THE PRELIMINARY ANSWERS BELOW AND PROVIDE A STEP BY STEP SOLUTION FOR EACH PROBLEM. If the preliminary answer is incorrect please proceed with the explanation of the correct answer:

The NeverLost Company produces and sells popular and widely used portable GPS units for recreational use. Researchers at NeverLost have estimated that the point price elasticity of demand facing the company under current conditions is - 1.2 while the point income elasticity is 2.2 and the point cross-price elasticity of demand with respect to the price of a competitor’s GPS unit is 1.4. NeverLost’s current sales are 2.2 million units per year.

a. What are expected sales next year once a new tax law takes effect that is expected to lower the disposable income of consumers per month by 1%?

- Preliminary Answer: 12%annually Sales are expected to drop 26.2 percent. From 2.2 million units to 1,619,200.

b. After the tax law goes into effect, your competitor announces a 5% increase in the price of their GPS unit. What are NeverLost’s expected sales after the competitor’s new price takes effect?

- Preliminary Answer: Sales will increase by 7 percent. From 2.2 million to 2,354,000.

c. In order to capture a significantly larger share of the market for these units, NeverLost wants to increase its sales next year by 6%. By how much must NeverLost change its price to accomplish this goal?

- Preliminary Answer: Decrease price by 5 percent

Answer 1

The Neverlost company produces and sells popular and widely used portable GPS units for recreational use.

Researchers at Neverlost have estimated that the point income elasticity = 2.2

Neverlost’s current sales (Q₁) = 2.2 million units per year

1. Let the expected sales next year after the new tax law takes effect = Q₂

The new tax laws is expected to lower disposable income (DI) per month by 1%.

Assume that per month DI of the consumers = x, before the tax law.

After the tax laws are imposed, DI of the consumers per month = 0.99x

The annual income before the new tax law (Y₁) = 12x

The annual income after the new tax law (Y₂) = 11.88x

Therefore, % change in sales = (Q₂ – Q₁)/Q₁ = (Q₂ – 2.2)/2.2

% change in DI = (Y₂ – Y₁)/Y₁ = (11.88 – 12)/12 =-0.01

Income elasticity = (% change in sales)/(% change in DI)

Or, Q₂ = 2.1516

Thus, expected sales next year is going to fall from 2.2 million units to 2.1516 million units once the new tax laws are imposed.

1. After the tax law goes into effect, Neverlost’s competitor announces a 5% increase in the price of their GPS unit.

Researchers have estimated that the point cross-price elasticity of demand with respect to the price of a competitor’s GPS unit is 1.4.

After the tax laws, Q₁ = 2.1516

Let the expected sales of Neverlost after the competitor’s new price takes effect = Q₂

Let us assume the initial price of competitors (P₁) = x

So, when they raise their prices by 5%, the new price of the competitors (P₂) = 0.95x

Therefore, % change in sales = (Q₂ – Q₁)/Q₁ = (Q₂ – 2.1516)/2.1516

% change in competitors’ price = (x – 0.95)/x = 0.05

Cross price elasticity = (% change in sales)/(% change in competitors’ price)

Thus, expected sales next year is going to increase from 2.1516 million units to 2.3 million units once the competitor increases the prices of its products by 5%.

1. In order to capture a significantly larger share of the market for these units, NeverLost wants to increase its sales next year by 6%.

So, let us assume that initial quantity (Q1) = x

Neverlost wants to increase its sales next year by 6% such that new quantity (Q2) = 1.06

Let us again assume that initial price = P1

And new reduced price = P2

Researchers at NeverLost have estimated that the point price elasticity of demand facing the company under current conditions is - 1.2.

So, Neverlost must reduce price by 5% to accomplish this goal.